At Planck scale, space-time is quantum foam and has nodes, loops {quantum loop}, kinks, knots, intersections, and links, depending on spins. A loop theory {quantum loop theory}| {loop quantum gravity} can represent quantum-foam loops and their kinks (but not intersections, links, and knots).
Quantum-loop lengths are multiples of Planck length. Quantum-loop areas are multiples of Planck area. Quantum-loop volumes are multiples of Planck volume.
Because spins can transfer, quantum loops can interact. Force fields have interacting quantum loops.
Quantum loops define space dimensions (background independent). Perhaps, space is intertwined quantum loops.
Interacting quantum loops can make fractals. Perhaps, space-time has fractal structure at Planck lengths. Fractals can remove the infinities that appear in relativity and quantum mechanics.
Quantum loop theory derives from general relativity and adds quantum mechanics. Quantum loop theory uses ideas of supergravity, twistor theory, string theory, and non-commutative geometries.
At quantum distances, quantum loops have repulsion.
photons
Loop quantum gravity predicts that high-energy photons, such as gamma rays, have faster speeds than low-energy photons, such as infrared rays. A test of this hypothesis is to measure if the microwave background radiation scatters photons. If photons all have same light speed, they scatter, but if some have faster speed, they do not scatter.
Quantum loop theory does not assume space-time existence {background independence, space}. Quantum loops determine matter and energy, which cause space-time geometry. In contrast, string theory assumes space-time (background dependence).
Behavior can be the same in any coordinate system {diffeomorphism invariance}.
In networks {spin network}|, nodes are space states, and edges connecting nodes are state transitions. Particle motions are translations from node to node, with possible momentum and angular-momentum changes. Transition series travel along edges {path, graph} {graph, path}. Therefore, spin networks are extensions of quantum mechanics and describe space-time quantum states and their transitions. They can approximate all space-time geometries, quantum states, and motions. Spin networks are about a single time.
nodes
Different node types represent different particles and their positions and angular momenta. Simple nodes are volume quanta. Networks have total volume equal to total angular momentum.
edges
Different edge types represent different fields, energies, or forces between masses. Simple lines between nodes are area quanta. Edge lines indicate momentum.
quantum loops
Spin networks can represent linked quantum loops and their possible kinks. Therefore, spin networks can approximate quantum foam. However, spin networks cannot represent quantum-foam intersections, links, or knots.
Spin networks can evolve in time {spin foam}|. Time is in multiples of Planck time. Spin-foam lines are nodes plus one quantized time dimension, and represent space-time states. Spin-foam surfaces are edges plus one quantized time dimension, and represent space-time state transitions. Spin-foam nodes are where spin-foam lines intersect and represent quanta. Spin foams are extensions of quantum mechanics and can represent electronic transitions and particle interactions. However, spin foams cannot represent quantum-foam intersections, links, or knots.
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Date Modified: 2022.0225